Looking at the jam submissions thus far, they're all playable in a browser. I'm not sure if I want to make a web client. It's certainly possible, Godot has various web export options, but it makes asset loading complicated for a reusable, general-purpose client.
Executable SOUPs build rooms and nights based on whatever folders are available in the filesystem, regardless of their names. A web client can't browse like that if it's going to work as an Itch upload. It would have to know the paths of all rooms ahead of time.
Maybe it's possible to inject assets into a Godot project after it's been compiled for web?